A non-convex variational problem appearing in a large deformation elasticity problem

TL;DR

This paper investigates global extrema in a complex nonconvex variational problem related to large deformation elasticity, providing improved and corrected results over previous findings using elementary methods.

Contribution

It offers a refined analysis of a nonsmooth nonconvex variational problem, correcting and enhancing prior results in the context of large deformation elasticity.

Findings

Improved characterization of global extrema in the variational problem.

Correction of a previous theorem by Gao and Ogden.

Elementary tools used for the analysis.

Abstract

A result concerning global extrema in a nonsmooth nonconvex variational problem that appears in applications (e.g. in a large deformation elasticity problem) is investigated in comparison with a result of D.Y. Gao and R.W. Ogden. The tools used are elementary and the results derived improve upon and correct a recent similar result, more precisely, Theorem 4 of the paper "Closed-form solutions, extremality and nonsmoothness criteria in a large deformation elasticity problem" by the fore-mentioned authors.